On vector bundles on 3-folds with sectional genus 1

Ballico, Edoardo

doi:10.1090/S0002-9947-1991-0986021-8

On vector bundles on $3$-folds with sectional genus $1$
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Trans. Amer. Math. Soc. 324 (1991), 135-147 Request permission

Abstract:

Here we give a classification (in characteristic zero) of pairs $(V,E)$ with $V$ being a smooth, connected, complete $3$-fold and $E$ a rank-$2$ spanned ample vector bundle on $V$ with sectional genus $1$. The proof uses the partial classification of Fano $3$-folds and Mori theory.

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Length of extremal rays and applications